Question

Sanvi purchased some books for Rs 120. If she had purchased 3 more books for the same amount each book would have cost her Rs 2 less. Find the number of books purchased by sanvi and the price of each book

Answer 1

Answer:12 books ,₹10

Step-by-step explanation:

Let the number of books be x.

And cost of each book =(120/x).

A.T.Q

Answer 2

Price of each book is Rs 10.

It is given that Sanvi purchased some books for Rs. 120

Let the number of books purchased by her be x.

So,  

The cost of each book = Rs. (20/x) ... (i)

Again, she purchases 3 more books for the same price .

Therefore, the number of books with Sanvi will be = (x+3) and,

The cost of each book will be = Rs [120/(x+3)] ... (ii)

It is given their differences would cost Rs 2 less. So,

[120/x] - [120/(x+3)] = 2

⇒ 120 [(x+3-x)/x(x+3)] = 2

⇒ 60 [3/(x² + 3x)] = 1

⇒ 180 = x² + 3x

⇒ x² + 3x - 180 = 0

⇒ x² + 15x - 12x - 180 = 0

⇒ x(x+15) - 12(x+15) = 0

⇒ (x + 15)(x - 12) = 0

By Zero Product Rule,

⇒ x = - 15 , which cannot be true as price cant be negative.

So, x = 12 is the number of books purchased by her.

∴ The cost of each book = 120/x = 120/12 = Rs. 10